library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
## ✓ ggplot2 3.3.5 ✓ purrr 0.3.4
## ✓ tibble 3.1.2 ✓ dplyr 1.0.7
## ✓ tidyr 1.1.3 ✓ stringr 1.4.0
## ✓ readr 1.4.0 ✓ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
library(broom)
library(broom.mixed)
library(stats)
library(lme4)
## Loading required package: Matrix
##
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack
library(lmerTest)
##
## Attaching package: 'lmerTest'
## The following object is masked from 'package:lme4':
##
## lmer
## The following object is masked from 'package:stats':
##
## step
PUF_ELIX_IP2009 <- read.csv("PUF_ELIX_IP2009.csv")
PUF_ELIX_IP2009 <- within(PUF_ELIX_IP2009, {
STATE <- factor(STATE)
COUNTY <- factor(COUNTY)
FULL_FIPS_CODE <- factor(FULL_FIPS_CODE)
CBSA <- factor(CBSA)
})
PUF_ELIX_IP2009 <- PUF_ELIX_IP2009 %>%
mutate(VISITS = TOTAL_VISITS>0)
Beginning Covariates:m1 <- glm(VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE, data=PUF_ELIX_IP2009, family=binomial(link="logit"))
summary(m1)
##
## Call:
## glm(formula = VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED +
## HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE,
## family = binomial(link = "logit"), data = PUF_ELIX_IP2009)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6333 -0.4555 -0.2246 -0.1804 3.0203
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.699990 0.067367 -54.923 < 2e-16 ***
## BENE_AGE -0.005143 0.000798 -6.445 1.16e-10 ***
## B_SEX 0.005323 0.020665 0.258 0.79674
## B_DIVERSE -0.051365 0.028395 -1.809 0.07046 .
## B_DIED 0.251596 0.078843 3.191 0.00142 **
## HF_PROP_RANK 0.057217 0.054299 1.054 0.29200
## HO_PROP_RANK -0.066118 0.057123 -1.157 0.24709
## TOTCHRONIC 0.413353 0.004435 93.200 < 2e-16 ***
## MEAN_ELIX_SCORE 0.475669 0.005182 91.794 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 93906 on 110329 degrees of freedom
## Residual deviance: 64097 on 110321 degrees of freedom
## (1852 observations deleted due to missingness)
## AIC: 64115
##
## Number of Fisher Scoring iterations: 6
In this model,
Age, Total # of Chronic Conditions and Mean Elixhauser Score are significant at the 99% CI against the outcome of having any inpatient “VISITS”.
As age goes up, the likelihood of any visit goes down. At some point, people die.
As the # of chronic conditions & mean Elixhauser scores increase the likelihood of any inpatient visits increase.
Whether or not the person Died in 2009 is significant at the 95% CI.
People often die in the hospital, so dying and inpatient visits are significantly related.
Not being white (B_DIVERSE) is significant at the 90% CI.
The estimate is negative, so there is a negative relationship between being not white and having visits.
Inverse relationships in correlation matrices show that there is a negative relationship between being a person of color and living longer, also system utilization / going to the doctor regularly.
Now that we’ve looked at the outcome of any “VISITS”, we can look at the outcome of TOTAL_VISITS>0
PUF_ELIX_IP2009_GT0 <- subset(PUF_ELIX_IP2009, TOTAL_VISITS>0)
The original data set had 113,305 observations, and this subset has 16,908.
First, let’s try OLS against the outcome of TOTAL_VISITS > 0. Then,
We will try a Poisson model with log link for the observations.
# Could be worse ... but standardized residual plots look pretty wonky!!
m0 <- lm(TOTAL_VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE, data=PUF_ELIX_IP2009_GT0)
summary(m0)
##
## Call:
## lm(formula = TOTAL_VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED +
## HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE,
## data = PUF_ELIX_IP2009_GT0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0379 -0.3597 -0.1659 0.2019 2.8953
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.7239201 0.0287808 25.153 <2e-16 ***
## BENE_AGE -0.0002269 0.0003318 -0.684 0.494
## B_SEX 0.0069197 0.0085893 0.806 0.420
## B_DIVERSE 0.0189714 0.0118204 1.605 0.109
## B_DIED 0.3027413 0.0310598 9.747 <2e-16 ***
## HF_PROP_RANK 0.0006657 0.0224746 0.030 0.976
## HO_PROP_RANK -0.0140451 0.0235501 -0.596 0.551
## TOTCHRONIC 0.0870507 0.0020450 42.568 <2e-16 ***
## MEAN_ELIX_SCORE 0.0468164 0.0020604 22.722 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5467 on 16723 degrees of freedom
## (175 observations deleted due to missingness)
## Multiple R-squared: 0.1414, Adjusted R-squared: 0.141
## F-statistic: 344.2 on 8 and 16723 DF, p-value: < 2.2e-16
plot(m0)
The OLS / Gaussian model is a poor fit.
m2 <- glm(TOTAL_VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE, data=PUF_ELIX_IP2009_GT0, family=poisson(link = "log"))
summary(m2)
##
## Call:
## glm(formula = TOTAL_VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED +
## HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE,
## family = poisson(link = "log"), data = PUF_ELIX_IP2009_GT0)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9085 -0.3100 -0.1467 0.1304 2.1249
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.2020799 0.0466156 -4.335 1.46e-05 ***
## BENE_AGE -0.0001485 0.0005293 -0.281 0.779
## B_SEX 0.0049213 0.0137592 0.358 0.721
## B_DIVERSE 0.0141917 0.0188282 0.754 0.451
## B_DIED 0.2043975 0.0447024 4.572 4.82e-06 ***
## HF_PROP_RANK 0.0002444 0.0359756 0.007 0.995
## HO_PROP_RANK -0.0099202 0.0376879 -0.263 0.792
## TOTCHRONIC 0.0681299 0.0033237 20.498 < 2e-16 ***
## MEAN_ELIX_SCORE 0.0357517 0.0032438 11.021 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 3669.4 on 16731 degrees of freedom
## Residual deviance: 3034.6 on 16723 degrees of freedom
## (175 observations deleted due to missingness)
## AIC: 39373
##
## Number of Fisher Scoring iterations: 4
Age is no longer significant in this model.
Death, Chronic Conditions and Elixhauser Score remain significant.
Let’s compare this Poisson model to a Negative Binomial model.
library(MASS)
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
m3 <- glm.nb(TOTAL_VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE, data=PUF_ELIX_IP2009_GT0)
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
summary(m3)
##
## Call:
## glm.nb(formula = TOTAL_VISITS ~ BENE_AGE + B_SEX + B_DIVERSE +
## B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE,
## data = PUF_ELIX_IP2009_GT0, init.theta = 118176.1914, link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9085 -0.3100 -0.1467 0.1304 2.1249
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.2020797 0.0466160 -4.335 1.46e-05 ***
## BENE_AGE -0.0001485 0.0005293 -0.281 0.779
## B_SEX 0.0049212 0.0137593 0.358 0.721
## B_DIVERSE 0.0141917 0.0188283 0.754 0.451
## B_DIED 0.2043973 0.0447029 4.572 4.82e-06 ***
## HF_PROP_RANK 0.0002444 0.0359759 0.007 0.995
## HO_PROP_RANK -0.0099201 0.0376882 -0.263 0.792
## TOTCHRONIC 0.0681299 0.0033237 20.498 < 2e-16 ***
## MEAN_ELIX_SCORE 0.0357517 0.0032438 11.021 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(118176.2) family taken to be 1)
##
## Null deviance: 3669.3 on 16731 degrees of freedom
## Residual deviance: 3034.5 on 16723 degrees of freedom
## (175 observations deleted due to missingness)
## AIC: 39375
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 118176
## Std. Err.: 170345
## Warning while fitting theta: iteration limit reached
##
## 2 x log-likelihood: -39354.98
And finally, let’s fit the original data to a Zero-Inflated Negative Binomial model
library(pscl)
## Classes and Methods for R developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University
## Simon Jackman
## hurdle and zeroinfl functions by Achim Zeileis
m4 <- zeroinfl(TOTAL_VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE,
data = PUF_ELIX_IP2009, dist = "negbin")
summary(m4)
##
## Call:
## zeroinfl(formula = TOTAL_VISITS ~ BENE_AGE + B_SEX + B_DIVERSE + B_DIED +
## HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE, data = PUF_ELIX_IP2009,
## dist = "negbin")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -1.68015 -0.34172 -0.11074 -0.08544 30.89873
##
## Count model coefficients (negbin with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.2930409 0.0527404 -43.478 < 2e-16 ***
## BENE_AGE -0.0018493 0.0005757 -3.212 0.00132 **
## B_SEX 0.0246383 0.0150825 1.634 0.10235
## B_DIVERSE 0.0212150 0.0206331 1.028 0.30385
## B_DIED 0.3635194 0.0489567 7.425 1.13e-13 ***
## HF_PROP_RANK 0.0378638 0.0394239 0.960 0.33684
## HO_PROP_RANK -0.0648401 0.0414014 -1.566 0.11732
## TOTCHRONIC 0.2441284 0.0035428 68.908 < 2e-16 ***
## MEAN_ELIX_SCORE 0.1583228 0.0041000 38.615 < 2e-16 ***
## Log(theta) 14.0213433 18.6855791 0.750 0.45302
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.591730 0.212105 7.504 6.17e-14 ***
## BENE_AGE 0.008951 0.002618 3.420 0.000627 ***
## B_SEX 0.102321 0.064578 1.584 0.113090
## B_DIVERSE 0.211687 0.087673 2.415 0.015756 *
## B_DIED 0.316981 0.241339 1.313 0.189038
## HF_PROP_RANK 0.047620 0.169204 0.281 0.778377
## HO_PROP_RANK -0.153982 0.178558 -0.862 0.388485
## TOTCHRONIC -0.223664 0.015084 -14.828 < 2e-16 ***
## MEAN_ELIX_SCORE -2.191743 0.080080 -27.369 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Theta = 1228547.7199
## Number of iterations in BFGS optimization: 34
## Log-likelihood: -4.173e+04 on 19 Df
As you can see, we could have jumped straight to the Zero-Inflated model, as it contains the hurdle model!
Let’s look at some of the plots.
# Diagnostic and Residuals plot for m2: Poisson regression (over dispersion is evident)
plot(m2)
# Diagnostic and Residuals plot for m3: Negative Binomial regression (still over dispersed)
plot(m3)
# Negative Binomial
ggplot(data = PUF_ELIX_IP2009_GT0, aes(x = TOTCHRONIC, y = TOTAL_VISITS)) +
geom_jitter(height=0.05, width = 0.1) +
stat_smooth(method = "glm.nb")
## `geom_smooth()` using formula 'y ~ x'
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
# Poisson
ggplot(data = PUF_ELIX_IP2009_GT0, aes(x = TOTCHRONIC, y = TOTAL_VISITS)) +
geom_jitter(height=0.05, width = 0.1) +
stat_smooth(method = "glm", method.args = c(family="poisson"))
## `geom_smooth()` using formula 'y ~ x'
They’re basically identical.
# Negative Binomial
ggplot(data = PUF_ELIX_IP2009_GT0, aes(x = MEAN_ELIX_SCORE, y = TOTAL_VISITS)) +
geom_jitter(height=0.05, width = 0.1) +
stat_smooth(method = "glm.nb")
## `geom_smooth()` using formula 'y ~ x'
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
# Poisson
ggplot(data = PUF_ELIX_IP2009_GT0, aes(x = MEAN_ELIX_SCORE, y = TOTAL_VISITS)) +
geom_jitter(height=0.05, width = 0.1) +
stat_smooth(method = "glm", method.args = c(family="poisson"))
## `geom_smooth()` using formula 'y ~ x'
These are very similar.
Based on the dispersion handling, the zero-inflated model was the most accurate thus far,
but let’s look at some different covariates, using the Poisson model.
What else could be related to the total # of inpatient visits?
# Can't use TOTAL_PHYS or TOTAL_CODES due to their near-perfect correlation with the outcome variable (see python corr matrix)
m2b <- glm(TOTAL_VISITS ~ BENE_AGE + B_DIVERSE + B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE + CVRG_MOS + RX_CVRG_MOS + TOTAL_LOS, data=PUF_ELIX_IP2009_GT0, family=poisson(link = "log"))
summary(m2b)
##
## Call:
## glm(formula = TOTAL_VISITS ~ BENE_AGE + B_DIVERSE + B_DIED +
## HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE +
## CVRG_MOS + RX_CVRG_MOS + TOTAL_LOS, family = poisson(link = "log"),
## data = PUF_ELIX_IP2009_GT0)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.47013 -0.22946 -0.09558 0.07130 1.95714
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.654e-01 9.852e-02 -2.694 0.00706 **
## BENE_AGE -3.128e-05 5.262e-04 -0.059 0.95260
## B_DIVERSE 4.418e-03 1.884e-02 0.235 0.81455
## B_DIED 1.462e-01 4.476e-02 3.267 0.00109 **
## HF_PROP_RANK -1.167e-03 3.600e-02 -0.032 0.97414
## HO_PROP_RANK -3.371e-03 3.774e-02 -0.089 0.92883
## TOTCHRONIC 4.371e-02 3.450e-03 12.670 < 2e-16 ***
## MEAN_ELIX_SCORE 1.959e-02 3.317e-03 5.906 3.51e-09 ***
## CVRG_MOS 1.675e-03 7.327e-03 0.229 0.81915
## RX_CVRG_MOS 1.290e-03 1.720e-03 0.750 0.45322
## TOTAL_LOS 2.829e-02 8.923e-04 31.703 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 3669.4 on 16731 degrees of freedom
## Residual deviance: 2156.8 on 16721 degrees of freedom
## (175 observations deleted due to missingness)
## AIC: 38499
##
## Number of Fisher Scoring iterations: 4
Now, let’s see what impact State and County or CBSA would have.
m2c <- glm(TOTAL_VISITS ~ BENE_AGE + B_DIVERSE + B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE + TOTAL_LOS + STATE, data=PUF_ELIX_IP2009_GT0, family=poisson(link = "log"))
summary(m2c)
##
## Call:
## glm(formula = TOTAL_VISITS ~ BENE_AGE + B_DIVERSE + B_DIED +
## HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE +
## TOTAL_LOS + STATE, family = poisson(link = "log"), data = PUF_ELIX_IP2009_GT0)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.45431 -0.22923 -0.09585 0.07105 1.95996
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.229e-01 6.572e-02 -3.391 0.000697 ***
## BENE_AGE -4.833e-05 5.282e-04 -0.091 0.927104
## B_DIVERSE 3.524e-03 1.929e-02 0.183 0.855078
## B_DIED 1.458e-01 4.489e-02 3.247 0.001165 **
## HF_PROP_RANK 3.099e-03 3.833e-02 0.081 0.935568
## HO_PROP_RANK -7.839e-03 4.055e-02 -0.193 0.846697
## TOTCHRONIC 4.386e-02 3.437e-03 12.759 < 2e-16 ***
## MEAN_ELIX_SCORE 1.957e-02 3.322e-03 5.892 3.83e-09 ***
## TOTAL_LOS 2.832e-02 8.951e-04 31.642 < 2e-16 ***
## STATEAlaska 3.373e-02 1.783e-01 0.189 0.849975
## STATEArizona -3.518e-02 7.256e-02 -0.485 0.627764
## STATEArkansas -3.369e-03 7.795e-02 -0.043 0.965530
## STATECalifornia -1.741e-03 5.368e-02 -0.032 0.974129
## STATEColorado -1.584e-02 7.701e-02 -0.206 0.837059
## STATEConnecticut -7.701e-04 8.125e-02 -0.009 0.992437
## STATEDelaware -8.329e-03 1.266e-01 -0.066 0.947555
## STATEDistrict of Columbia -4.154e-04 1.610e-01 -0.003 0.997941
## STATEFlorida -8.418e-03 5.432e-02 -0.155 0.876838
## STATEGeorgia 1.598e-03 6.204e-02 0.026 0.979450
## STATEHawaii -2.357e-03 1.261e-01 -0.019 0.985087
## STATEIdaho 6.570e-03 1.124e-01 0.058 0.953389
## STATEIllinois -9.086e-03 5.785e-02 -0.157 0.875207
## STATEIndiana -1.101e-02 6.505e-02 -0.169 0.865647
## STATEIowa -1.995e-02 7.905e-02 -0.252 0.800749
## STATEKansas -6.933e-02 8.411e-02 -0.824 0.409816
## STATEKentucky -9.691e-03 6.953e-02 -0.139 0.889152
## STATELouisiana -1.039e-02 7.232e-02 -0.144 0.885782
## STATEMaine -7.726e-03 9.895e-02 -0.078 0.937767
## STATEMaryland 7.252e-03 6.953e-02 0.104 0.916924
## STATEMassachusetts -2.879e-02 6.451e-02 -0.446 0.655398
## STATEMichigan -6.699e-03 5.911e-02 -0.113 0.909776
## STATEMinnesota 9.549e-03 7.240e-02 0.132 0.895067
## STATEMississippi -2.220e-02 7.367e-02 -0.301 0.763129
## STATEMissouri -1.074e-02 6.586e-02 -0.163 0.870468
## STATEMontana -3.387e-03 1.322e-01 -0.026 0.979564
## STATENebraska -7.422e-02 9.288e-02 -0.799 0.424217
## STATENevada -5.976e-02 9.925e-02 -0.602 0.547103
## STATENew Hampshire -8.496e-02 1.093e-01 -0.778 0.436822
## STATENew Jersey 6.841e-05 6.161e-02 0.001 0.999114
## STATENew Mexico -1.578e-02 1.064e-01 -0.148 0.882135
## STATENew York -1.869e-02 5.575e-02 -0.335 0.737502
## STATENorth Carolina -1.092e-02 6.091e-02 -0.179 0.857768
## STATENorth Dakota 8.357e-02 1.305e-01 0.640 0.521923
## STATEOhio -4.039e-03 5.844e-02 -0.069 0.944893
## STATEOklahoma 3.336e-02 7.448e-02 0.448 0.654260
## STATEOregon -2.961e-02 8.336e-02 -0.355 0.722473
## STATEPennsylvania 2.958e-03 5.747e-02 0.051 0.958948
## STATERhode Island -4.776e-02 1.255e-01 -0.381 0.703450
## STATESouth Carolina -2.662e-03 6.984e-02 -0.038 0.969596
## STATESouth Dakota -4.225e-02 1.297e-01 -0.326 0.744577
## STATETennessee -4.676e-02 6.523e-02 -0.717 0.473507
## STATETexas 1.154e-02 5.500e-02 0.210 0.833866
## STATEUtah -8.078e-03 1.036e-01 -0.078 0.937859
## STATEVermont -5.687e-02 1.552e-01 -0.366 0.714037
## STATEVirginia -3.215e-02 6.444e-02 -0.499 0.617847
## STATEWashington -4.231e-02 6.926e-02 -0.611 0.541304
## STATEWest Virginia 7.322e-02 8.493e-02 0.862 0.388607
## STATEWisconsin -5.365e-04 6.801e-02 -0.008 0.993706
## STATEWyoming -1.627e-02 1.568e-01 -0.104 0.917394
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 3669.4 on 16731 degrees of freedom
## Residual deviance: 2148.5 on 16673 degrees of freedom
## (175 observations deleted due to missingness)
## AIC: 38587
##
## Number of Fisher Scoring iterations: 4
No significant states. Let’s try CBSAs.
m2e <- glm(TOTAL_VISITS ~ BENE_AGE + B_DIVERSE + B_DIED + HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE + RX_CVRG_MOS + TOTAL_LOS + CBSA, data=PUF_ELIX_IP2009_GT0, family=Gamma(link = "log"))
summary(m2e)
##
## Call:
## glm(formula = TOTAL_VISITS ~ BENE_AGE + B_DIVERSE + B_DIED +
## HF_PROP_RANK + HO_PROP_RANK + TOTCHRONIC + MEAN_ELIX_SCORE +
## RX_CVRG_MOS + TOTAL_LOS + CBSA, family = Gamma(link = "log"),
## data = PUF_ELIX_IP2009_GT0)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.79865 -0.19922 -0.08349 0.06562 1.40956
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.200e-01 1.796e-02 -12.251 < 2e-16 ***
## BENE_AGE 1.427e-05 1.915e-04 0.075 0.94058
## B_DIVERSE 4.897e-03 6.934e-03 0.706 0.48004
## B_DIED 1.374e-01 1.793e-02 7.662 1.93e-14 ***
## HF_PROP_RANK 1.245e-02 1.840e-02 0.677 0.49865
## HO_PROP_RANK -1.783e-02 1.865e-02 -0.957 0.33882
## TOTCHRONIC 3.665e-02 1.225e-03 29.930 < 2e-16 ***
## MEAN_ELIX_SCORE 1.704e-02 1.207e-03 14.116 < 2e-16 ***
## RX_CVRG_MOS 8.316e-04 6.053e-04 1.374 0.16948
## TOTAL_LOS 3.161e-02 4.130e-04 76.528 < 2e-16 ***
## CBSA10180 2.063e-01 8.716e-02 2.367 0.01793 *
## CBSA10420 1.350e-02 4.864e-02 0.277 0.78141
## CBSA10500 -4.525e-02 9.031e-02 -0.501 0.61633
## CBSA10580 -3.526e-03 4.807e-02 -0.073 0.94153
## CBSA10740 5.629e-03 5.110e-02 0.110 0.91230
## CBSA10780 2.706e-02 9.439e-02 0.287 0.77438
## CBSA10900 -4.473e-02 4.071e-02 -1.099 0.27181
## CBSA11020 6.080e-02 9.922e-02 0.613 0.54002
## CBSA11100 -1.261e-01 8.681e-02 -1.452 0.14649
## CBSA11180 -1.334e-01 1.399e-01 -0.954 0.34026
## CBSA11260 3.009e-02 7.622e-02 0.395 0.69298
## CBSA11300 -8.264e-02 8.688e-02 -0.951 0.34147
## CBSA11340 -5.405e-02 8.690e-02 -0.622 0.53396
## CBSA11460 9.511e-02 7.404e-02 1.285 0.19897
## CBSA11500 -1.443e-02 9.900e-02 -0.146 0.88408
## CBSA11540 1.259e-02 1.398e-01 0.090 0.92826
## CBSA11700 -6.832e-02 5.497e-02 -1.243 0.21397
## CBSA12020 8.107e-02 1.399e-01 0.580 0.56222
## CBSA12060 5.941e-03 2.287e-02 0.260 0.79499
## CBSA12100 1.355e-02 9.042e-02 0.150 0.88087
## CBSA12220 4.768e-03 1.805e-01 0.026 0.97893
## CBSA12260 2.515e-03 5.164e-02 0.049 0.96116
## CBSA12420 1.120e-01 4.208e-02 2.661 0.00780 **
## CBSA12540 -5.175e-02 6.163e-02 -0.840 0.40110
## CBSA12580 3.042e-04 2.642e-02 0.012 0.99082
## CBSA12620 -1.091e-01 9.034e-02 -1.208 0.22720
## CBSA12700 3.685e-02 6.683e-02 0.551 0.58131
## CBSA12940 9.324e-03 5.406e-02 0.172 0.86307
## CBSA12980 1.344e-01 1.106e-01 1.215 0.22440
## CBSA13020 -2.486e-03 1.276e-01 -0.019 0.98446
## CBSA13140 -2.607e-02 6.156e-02 -0.423 0.67196
## CBSA13380 -1.036e-01 9.046e-02 -1.145 0.25228
## CBSA13460 7.974e-02 1.044e-01 0.764 0.44496
## CBSA13644 4.349e-02 4.572e-02 0.951 0.34146
## CBSA13740 -1.727e-02 9.895e-02 -0.175 0.86143
## CBSA13780 4.656e-02 7.193e-02 0.647 0.51748
## CBSA13820 1.906e-02 3.535e-02 0.539 0.58968
## CBSA13900 6.261e-03 9.901e-02 0.063 0.94958
## CBSA13980 -6.874e-02 8.087e-02 -0.850 0.39533
## CBSA14020 -1.059e-01 9.430e-02 -1.124 0.26123
## CBSA14060 1.149e-02 1.183e-01 0.097 0.92260
## CBSA14260 -4.319e-02 6.689e-02 -0.646 0.51847
## CBSA14484 -2.021e-02 3.071e-02 -0.658 0.51044
## CBSA14500 2.888e-02 9.050e-02 0.319 0.74961
## CBSA14540 7.729e-02 1.398e-01 0.553 0.58039
## CBSA14740 -1.168e-01 9.437e-02 -1.237 0.21602
## CBSA14860 -4.225e-02 5.551e-02 -0.761 0.44665
## CBSA15180 2.988e-02 6.651e-02 0.449 0.65327
## CBSA15260 1.557e-01 1.563e-01 0.996 0.31928
## CBSA15380 6.870e-02 4.076e-02 1.686 0.09191 .
## CBSA15500 -8.876e-02 1.182e-01 -0.751 0.45263
## CBSA15540 -2.147e-02 1.182e-01 -0.182 0.85587
## CBSA15764 -2.191e-02 3.329e-02 -0.658 0.51046
## CBSA15804 4.231e-04 3.828e-02 0.011 0.99118
## CBSA15940 3.923e-03 5.925e-02 0.066 0.94721
## CBSA15980 2.933e-03 4.748e-02 0.062 0.95074
## CBSA16020 7.334e-03 8.369e-02 0.088 0.93017
## CBSA16180 2.742e-01 1.562e-01 1.755 0.07921 .
## CBSA16220 5.879e-02 1.105e-01 0.532 0.59483
## CBSA16300 -6.216e-02 6.537e-02 -0.951 0.34169
## CBSA16580 -8.000e-02 1.276e-01 -0.627 0.53079
## CBSA16620 6.249e-04 6.561e-02 0.010 0.99240
## CBSA16700 1.656e-01 5.183e-02 3.194 0.00140 **
## CBSA16740 -3.385e-02 3.427e-02 -0.988 0.32329
## CBSA16820 -8.233e-02 7.835e-02 -1.051 0.29337
## CBSA16860 -6.139e-02 5.332e-02 -1.151 0.24958
## CBSA16940 3.225e-02 1.398e-01 0.231 0.81748
## CBSA16974 -1.001e-02 1.621e-02 -0.617 0.53703
## CBSA17020 -9.520e-03 1.182e-01 -0.081 0.93579
## CBSA17140 -1.956e-02 2.827e-02 -0.692 0.48895
## CBSA17300 1.421e-02 8.379e-02 0.170 0.86532
## CBSA17420 1.277e-01 8.094e-02 1.578 0.11466
## CBSA17460 -2.554e-02 2.778e-02 -0.920 0.35780
## CBSA17660 1.720e-01 1.276e-01 1.348 0.17776
## CBSA17780 2.605e-01 2.209e-01 1.179 0.23836
## CBSA17820 3.677e-03 5.823e-02 0.063 0.94965
## CBSA17860 3.178e-01 1.107e-01 2.871 0.00409 **
## CBSA17900 -2.428e-02 5.329e-02 -0.456 0.64862
## CBSA17980 -1.088e-01 8.681e-02 -1.253 0.21014
## CBSA18020 1.016e-01 1.106e-01 0.919 0.35834
## CBSA18140 2.945e-02 3.284e-02 0.897 0.36986
## CBSA18580 6.387e-02 5.924e-02 1.078 0.28099
## CBSA18700 3.088e-02 3.124e-01 0.099 0.92126
## CBSA18880 3.411e-02 1.044e-01 0.327 0.74386
## CBSA19060 -3.655e-02 1.277e-01 -0.286 0.77464
## CBSA19124 3.672e-02 2.629e-02 1.397 0.16254
## CBSA19140 -1.809e-01 1.107e-01 -1.634 0.10224
## CBSA19180 -2.675e-01 1.277e-01 -2.096 0.03614 *
## CBSA19260 1.383e-01 9.040e-02 1.530 0.12592
## CBSA19340 1.692e-01 7.008e-02 2.415 0.01575 *
## CBSA19380 -1.943e-03 4.323e-02 -0.045 0.96415
## CBSA19460 -8.210e-02 8.377e-02 -0.980 0.32710
## CBSA19500 -6.733e-02 1.277e-01 -0.527 0.59792
## CBSA19660 -2.127e-02 4.791e-02 -0.444 0.65703
## CBSA19740 -5.435e-03 3.116e-02 -0.174 0.86153
## CBSA19780 -1.536e-02 5.567e-02 -0.276 0.78266
## CBSA19804 -4.410e-02 2.801e-02 -1.574 0.11545
## CBSA20020 6.476e-02 8.688e-02 0.745 0.45608
## CBSA20100 -1.171e-01 9.912e-02 -1.181 0.23763
## CBSA20220 5.485e-02 1.182e-01 0.464 0.64273
## CBSA20260 -1.287e-01 8.375e-02 -1.537 0.12426
## CBSA20500 -1.839e-02 6.170e-02 -0.298 0.76567
## CBSA20740 -1.299e-01 1.182e-01 -1.099 0.27167
## CBSA20764 1.729e-02 2.808e-02 0.616 0.53808
## CBSA20940 2.337e-01 1.107e-01 2.112 0.03472 *
## CBSA21060 1.673e-01 1.107e-01 1.512 0.13061
## CBSA21140 3.301e-02 1.048e-01 0.315 0.75272
## CBSA21300 -1.290e-01 1.563e-01 -0.825 0.40928
## CBSA21340 -6.132e-03 5.375e-02 -0.114 0.90916
## CBSA21500 4.269e-02 7.637e-02 0.559 0.57614
## CBSA21660 -1.452e-01 8.079e-02 -1.797 0.07241 .
## CBSA21780 -5.174e-02 7.029e-02 -0.736 0.46162
## CBSA21820 -2.118e-01 1.804e-01 -1.174 0.24044
## CBSA22020 -1.231e-01 1.044e-01 -1.179 0.23830
## CBSA22140 -6.267e-02 1.805e-01 -0.347 0.72849
## CBSA22180 7.547e-02 7.184e-02 1.051 0.29348
## CBSA22220 1.637e-02 6.703e-02 0.244 0.80706
## CBSA22380 -8.428e-02 1.106e-01 -0.762 0.44606
## CBSA22420 -3.014e-03 6.415e-02 -0.047 0.96252
## CBSA22500 -7.560e-03 8.684e-02 -0.087 0.93062
## CBSA22520 -1.068e-01 9.896e-02 -1.079 0.28066
## CBSA22540 4.562e-02 1.276e-01 0.357 0.72077
## CBSA22660 -3.477e-02 6.414e-02 -0.542 0.58778
## CBSA22744 -1.128e-02 3.268e-02 -0.345 0.72999
## CBSA22900 4.958e-02 6.842e-02 0.725 0.46866
## CBSA23060 8.054e-02 6.151e-02 1.309 0.19040
## CBSA23104 4.179e-03 3.533e-02 0.118 0.90584
## CBSA23420 4.717e-02 5.655e-02 0.834 0.40418
## CBSA23460 -7.451e-02 1.042e-01 -0.715 0.47471
## CBSA23540 1.074e-01 8.685e-02 1.237 0.21622
## CBSA23580 2.630e-01 9.448e-02 2.783 0.00539 **
## CBSA23844 2.916e-02 4.746e-02 0.614 0.53893
## CBSA24020 7.196e-02 8.364e-02 0.860 0.38960
## CBSA24140 6.842e-02 1.276e-01 0.536 0.59185
## CBSA24220 -1.592e-01 1.277e-01 -1.247 0.21248
## CBSA24300 7.302e-02 9.032e-02 0.808 0.41883
## CBSA24340 -2.053e-02 4.374e-02 -0.469 0.63882
## CBSA24500 1.412e-01 1.106e-01 1.277 0.20168
## CBSA24540 -8.998e-02 1.563e-01 -0.576 0.56479
## CBSA24580 -6.194e-02 9.034e-02 -0.686 0.49296
## CBSA24660 -7.857e-02 4.983e-02 -1.577 0.11486
## CBSA24780 1.647e-01 1.563e-01 1.054 0.29194
## CBSA24860 -1.914e-02 4.714e-02 -0.406 0.68475
## CBSA25060 -1.813e-01 6.838e-02 -2.652 0.00802 **
## CBSA25180 1.432e-01 6.538e-02 2.190 0.02852 *
## CBSA25260 -2.269e-01 3.124e-01 -0.726 0.46767
## CBSA25420 9.453e-03 5.390e-02 0.175 0.86080
## CBSA25500 9.008e-02 9.440e-02 0.954 0.33999
## CBSA25540 3.946e-02 3.796e-02 1.040 0.29855
## CBSA25620 -4.831e-02 8.685e-02 -0.556 0.57804
## CBSA25860 5.716e-02 5.388e-02 1.061 0.28871
## CBSA25980 -3.831e-01 3.125e-01 -1.226 0.22017
## CBSA26100 -3.510e-02 6.706e-02 -0.523 0.60067
## CBSA26180 -6.240e-04 4.663e-02 -0.013 0.98932
## CBSA26300 -4.481e-02 8.392e-02 -0.534 0.59343
## CBSA26380 -6.305e-03 8.091e-02 -0.078 0.93789
## CBSA26420 2.744e-02 2.275e-02 1.206 0.22789
## CBSA26580 -3.036e-02 5.949e-02 -0.510 0.60985
## CBSA26620 4.109e-02 6.706e-02 0.613 0.54003
## CBSA26820 -7.029e-02 1.398e-01 -0.503 0.61515
## CBSA26900 2.607e-02 3.136e-02 0.831 0.40579
## CBSA26980 3.622e-01 1.805e-01 2.007 0.04481 *
## CBSA27060 -1.592e-01 1.563e-01 -1.018 0.30847
## CBSA27100 -9.886e-02 1.106e-01 -0.894 0.37135
## CBSA27140 1.808e-02 5.661e-02 0.319 0.74937
## CBSA27180 -6.696e-02 1.043e-01 -0.642 0.52081
## CBSA27260 -3.862e-02 3.944e-02 -0.979 0.32751
## CBSA27340 -1.816e-01 1.278e-01 -1.421 0.15531
## CBSA27500 9.930e-03 1.276e-01 0.078 0.93799
## CBSA27620 1.876e-02 1.106e-01 0.170 0.86528
## CBSA27740 4.750e-02 8.377e-02 0.567 0.57075
## CBSA27780 -1.093e-01 7.394e-02 -1.478 0.13948
## CBSA27860 -1.800e-02 2.209e-01 -0.081 0.93505
## CBSA27900 -8.769e-02 1.182e-01 -0.742 0.45823
## CBSA28020 -2.265e-02 6.548e-02 -0.346 0.72940
## CBSA28100 6.461e-02 1.182e-01 0.547 0.58461
## CBSA28140 1.565e-03 2.962e-02 0.053 0.95787
## CBSA28420 3.091e-02 8.366e-02 0.370 0.71174
## CBSA28660 7.286e-02 7.604e-02 0.958 0.33799
## CBSA28700 2.148e-02 5.935e-02 0.362 0.71746
## CBSA28740 2.066e-01 1.105e-01 1.869 0.06166 .
## CBSA28940 -3.699e-02 4.993e-02 -0.741 0.45887
## CBSA29020 -1.136e-01 1.105e-01 -1.028 0.30416
## CBSA29100 4.661e-02 9.055e-02 0.515 0.60673
## CBSA29140 7.764e-02 1.043e-01 0.744 0.45673
## CBSA29180 5.036e-02 8.380e-02 0.601 0.54785
## CBSA29340 3.252e-01 1.563e-01 2.081 0.03743 *
## CBSA29404 6.370e-02 4.757e-02 1.339 0.18055
## CBSA29420 8.849e-03 8.689e-02 0.102 0.91889
## CBSA29460 3.109e-02 4.596e-02 0.676 0.49875
## CBSA29540 -8.085e-02 5.748e-02 -1.407 0.15955
## CBSA29620 -6.053e-02 6.273e-02 -0.965 0.33462
## CBSA29700 -3.211e-02 9.150e-02 -0.351 0.72565
## CBSA29740 7.462e-03 9.921e-02 0.075 0.94004
## CBSA29820 -3.746e-02 3.888e-02 -0.964 0.33522
## CBSA29940 -2.719e-01 1.399e-01 -1.943 0.05202 .
## CBSA30020 9.360e-02 1.107e-01 0.846 0.39774
## CBSA30140 2.702e-02 1.277e-01 0.212 0.83236
## CBSA30300 -2.240e-01 1.804e-01 -1.242 0.21438
## CBSA30340 2.327e-01 1.398e-01 1.665 0.09587 .
## CBSA30460 -3.149e-02 5.949e-02 -0.529 0.59664
## CBSA30620 -1.250e-01 1.276e-01 -0.979 0.32738
## CBSA30700 -2.356e-02 7.026e-02 -0.335 0.73739
## CBSA30780 4.368e-02 5.480e-02 0.797 0.42546
## CBSA30860 -1.408e-01 2.209e-01 -0.637 0.52408
## CBSA30980 -2.462e-02 7.831e-02 -0.314 0.75325
## CBSA31020 -1.641e-01 1.398e-01 -1.174 0.24056
## CBSA31084 1.542e-02 1.912e-02 0.807 0.41993
## CBSA31140 -2.318e-02 3.833e-02 -0.605 0.54527
## CBSA31180 9.661e-02 1.043e-01 0.926 0.35446
## CBSA31340 -7.304e-02 7.829e-02 -0.933 0.35086
## CBSA31420 2.118e-02 1.106e-01 0.192 0.84812
## CBSA31460 1.320e-01 1.398e-01 0.944 0.34503
## CBSA31540 -6.989e-02 5.846e-02 -1.196 0.23190
## CBSA31700 -8.889e-02 7.005e-02 -1.269 0.20447
## CBSA31740 -2.770e-01 1.804e-01 -1.536 0.12466
## CBSA31860 -4.094e-02 1.277e-01 -0.321 0.74845
## CBSA31900 -2.156e-01 1.105e-01 -1.951 0.05110 .
## CBSA32580 -7.456e-02 5.577e-02 -1.337 0.18124
## CBSA32780 2.421e-01 1.182e-01 2.049 0.04045 *
## CBSA32820 1.774e-02 3.939e-02 0.450 0.65246
## CBSA32900 4.059e-02 1.563e-01 0.260 0.79507
## CBSA33124 -3.579e-02 2.948e-02 -1.214 0.22474
## CBSA33140 -9.469e-02 1.398e-01 -0.677 0.49816
## CBSA33260 -2.298e-01 1.398e-01 -1.643 0.10042
## CBSA33340 1.244e-02 3.229e-02 0.385 0.70017
## CBSA33460 -7.118e-03 2.790e-02 -0.255 0.79859
## CBSA33540 -3.547e-02 1.183e-01 -0.300 0.76424
## CBSA33660 -3.726e-02 6.554e-02 -0.569 0.56970
## CBSA33700 9.812e-03 6.537e-02 0.150 0.88069
## CBSA33740 -1.647e-01 9.433e-02 -1.746 0.08077 .
## CBSA33780 3.138e-01 1.106e-01 2.838 0.00455 **
## CBSA33860 -6.062e-02 6.155e-02 -0.985 0.32470
## CBSA34060 -9.938e-02 1.278e-01 -0.778 0.43673
## CBSA34100 1.771e-02 9.042e-02 0.196 0.84470
## CBSA34580 1.653e-01 9.891e-02 1.671 0.09473 .
## CBSA34620 -8.670e-02 1.043e-01 -0.831 0.40576
## CBSA34740 -2.334e-02 8.369e-02 -0.279 0.78029
## CBSA34820 -7.887e-02 7.597e-02 -1.038 0.29921
## CBSA34900 -1.272e-02 3.123e-01 -0.041 0.96752
## CBSA34940 8.095e-02 5.415e-02 1.495 0.13496
## CBSA34980 -1.845e-02 3.331e-02 -0.554 0.57963
## CBSA35004 -3.200e-02 2.602e-02 -1.230 0.21886
## CBSA35084 -6.104e-03 2.809e-02 -0.217 0.82800
## CBSA35300 2.518e-03 4.750e-02 0.053 0.95773
## CBSA35380 -3.278e-02 4.079e-02 -0.804 0.42160
## CBSA35644 -1.822e-02 1.440e-02 -1.265 0.20591
## CBSA35660 1.230e-01 9.431e-02 1.304 0.19227
## CBSA35840 -4.103e-02 3.678e-02 -1.116 0.26452
## CBSA35980 -1.940e-03 7.824e-02 -0.025 0.98022
## CBSA36084 -3.908e-02 3.370e-02 -1.160 0.24624
## CBSA36100 -2.020e-02 6.272e-02 -0.322 0.74734
## CBSA36140 -7.288e-02 9.436e-02 -0.772 0.43990
## CBSA36220 -4.370e-02 1.182e-01 -0.370 0.71161
## CBSA36260 4.754e-02 7.384e-02 0.644 0.51973
## CBSA36420 5.650e-02 3.809e-02 1.483 0.13800
## CBSA36500 1.404e-01 9.440e-02 1.488 0.13690
## CBSA36540 -4.502e-02 4.687e-02 -0.961 0.33680
## CBSA36740 -2.664e-02 2.904e-02 -0.917 0.35901
## CBSA36780 -1.353e-01 9.454e-02 -1.431 0.15231
## CBSA36980 -8.655e-03 9.440e-02 -0.092 0.92695
## CBSA37100 -1.050e-02 5.104e-02 -0.206 0.83703
## CBSA37340 5.896e-02 4.262e-02 1.383 0.16659
## CBSA37380 1.774e-01 1.182e-01 1.501 0.13348
## CBSA37460 -1.550e-01 9.435e-02 -1.642 0.10052
## CBSA37620 1.127e-02 9.436e-02 0.119 0.90489
## CBSA37700 3.985e-02 9.437e-02 0.422 0.67285
## CBSA37764 -4.762e-02 4.455e-02 -1.069 0.28519
## CBSA37860 -1.434e-02 4.965e-02 -0.289 0.77279
## CBSA37900 9.432e-02 5.567e-02 1.694 0.09023 .
## CBSA37964 2.685e-02 2.278e-02 1.178 0.23869
## CBSA38060 -2.969e-02 2.604e-02 -1.140 0.25431
## CBSA38220 2.313e-01 1.563e-01 1.480 0.13888
## CBSA38300 2.492e-02 2.521e-02 0.989 0.32287
## CBSA38340 2.879e-03 9.898e-02 0.029 0.97680
## CBSA38540 -7.889e-02 1.277e-01 -0.618 0.53673
## CBSA38860 1.769e-02 5.329e-02 0.332 0.73995
## CBSA38900 -3.140e-02 3.183e-02 -0.986 0.32396
## CBSA38940 -6.914e-02 5.557e-02 -1.244 0.21340
## CBSA39100 8.094e-02 5.475e-02 1.478 0.13930
## CBSA39140 5.048e-03 8.702e-02 0.058 0.95374
## CBSA39300 2.622e-03 3.165e-02 0.083 0.93398
## CBSA39340 -1.796e-01 9.442e-02 -1.903 0.05712 .
## CBSA39380 -1.146e-01 1.106e-01 -1.037 0.29998
## CBSA39460 -1.190e-01 8.369e-02 -1.422 0.15517
## CBSA39540 -9.359e-02 8.088e-02 -1.157 0.24723
## CBSA39580 4.262e-02 5.482e-02 0.777 0.43694
## CBSA39660 -6.808e-03 9.431e-02 -0.072 0.94246
## CBSA39740 -2.828e-03 7.013e-02 -0.040 0.96784
## CBSA39820 3.652e-02 1.105e-01 0.330 0.74108
## CBSA39900 -9.573e-02 7.015e-02 -1.365 0.17242
## CBSA40060 -6.924e-02 4.002e-02 -1.730 0.08364 .
## CBSA40140 1.062e-02 2.831e-02 0.375 0.70757
## CBSA40220 -4.389e-02 7.003e-02 -0.627 0.53080
## CBSA40340 -1.509e-01 1.277e-01 -1.182 0.23722
## CBSA40380 3.795e-02 3.755e-02 1.011 0.31223
## CBSA40420 -5.278e-03 6.401e-02 -0.082 0.93429
## CBSA40484 -5.887e-02 6.036e-02 -0.975 0.32943
## CBSA40580 -9.393e-02 1.562e-01 -0.601 0.54772
## CBSA40660 -3.809e-02 9.896e-02 -0.385 0.70032
## CBSA40900 4.263e-02 3.393e-02 1.257 0.20889
## CBSA40980 -6.363e-02 9.440e-02 -0.674 0.50026
## CBSA41060 -3.540e-03 1.043e-01 -0.034 0.97292
## CBSA41100 7.611e-03 1.398e-01 0.054 0.95658
## CBSA41140 3.651e-02 1.043e-01 0.350 0.72635
## CBSA41180 -2.804e-02 2.482e-02 -1.130 0.25859
## CBSA41420 1.483e-01 9.042e-02 1.641 0.10092
## CBSA41500 1.055e-01 8.690e-02 1.215 0.22454
## CBSA41540 -1.738e-01 1.106e-01 -1.571 0.11610
## CBSA41620 6.831e-03 4.291e-02 0.159 0.87351
## CBSA41660 -1.954e-02 9.038e-02 -0.216 0.82883
## CBSA41700 -4.552e-03 3.325e-02 -0.137 0.89112
## CBSA41740 -4.266e-02 2.977e-02 -1.433 0.15186
## CBSA41780 6.907e-02 1.805e-01 0.383 0.70199
## CBSA41884 -4.202e-02 3.204e-02 -1.312 0.18966
## CBSA41940 7.531e-02 4.247e-02 1.774 0.07616 .
## CBSA42020 -8.674e-02 8.376e-02 -1.036 0.30041
## CBSA42044 1.263e-02 2.939e-02 0.430 0.66737
## CBSA42060 -2.051e-02 5.931e-02 -0.346 0.72948
## CBSA42100 -6.000e-02 9.904e-02 -0.606 0.54465
## CBSA42140 -1.877e-01 1.277e-01 -1.469 0.14175
## CBSA42220 3.460e-02 6.414e-02 0.539 0.58962
## CBSA42340 6.356e-02 7.197e-02 0.883 0.37716
## CBSA42540 -9.764e-02 4.624e-02 -2.112 0.03471 *
## CBSA42644 -3.523e-02 3.018e-02 -1.167 0.24311
## CBSA42680 -3.958e-02 9.045e-02 -0.438 0.66170
## CBSA43100 -1.072e-01 1.182e-01 -0.907 0.36460
## CBSA43300 -1.849e-01 1.563e-01 -1.183 0.23699
## CBSA43340 1.269e-02 6.154e-02 0.206 0.83669
## CBSA43580 1.943e-01 1.398e-01 1.390 0.16466
## CBSA43620 -6.896e-02 8.097e-02 -0.852 0.39439
## CBSA43780 8.605e-03 7.824e-02 0.110 0.91243
## CBSA43900 -6.890e-02 7.388e-02 -0.933 0.35100
## CBSA44060 3.548e-02 6.402e-02 0.554 0.57947
## CBSA44100 -4.968e-02 7.832e-02 -0.634 0.52589
## CBSA44140 -1.215e-02 4.182e-02 -0.291 0.77134
## CBSA44180 8.930e-03 6.169e-02 0.145 0.88491
## CBSA44220 2.007e-01 1.562e-01 1.285 0.19890
## CBSA44300 2.067e-02 1.044e-01 0.198 0.84306
## CBSA44600 2.170e-02 9.035e-02 0.240 0.81018
## CBSA44700 -5.007e-02 6.851e-02 -0.731 0.46495
## CBSA44940 -6.766e-02 1.043e-01 -0.649 0.51656
## CBSA45060 -1.889e-02 5.239e-02 -0.361 0.71841
## CBSA45104 -3.663e-02 5.093e-02 -0.719 0.47207
## CBSA45220 -5.072e-02 7.830e-02 -0.648 0.51716
## CBSA45300 4.195e-03 2.457e-02 0.171 0.86442
## CBSA45460 -1.536e-01 8.682e-02 -1.769 0.07694 .
## CBSA45500 7.446e-02 1.042e-01 0.714 0.47495
## CBSA45780 1.436e-02 5.029e-02 0.286 0.77521
## CBSA45820 1.336e-01 1.398e-01 0.956 0.33929
## CBSA45940 6.435e-02 7.828e-02 0.822 0.41108
## CBSA46060 -7.105e-02 4.226e-02 -1.681 0.09270 .
## CBSA46140 2.594e-03 4.692e-02 0.055 0.95590
## CBSA46220 -7.421e-02 7.391e-02 -1.004 0.31539
## CBSA46340 -3.413e-02 7.598e-02 -0.449 0.65334
## CBSA46540 -1.121e-02 8.702e-02 -0.129 0.89754
## CBSA46660 -5.514e-02 1.182e-01 -0.467 0.64082
## CBSA46700 -9.762e-02 7.825e-02 -1.248 0.21220
## CBSA47020 -2.068e-01 1.277e-01 -1.619 0.10552
## CBSA47220 -1.161e-01 1.183e-01 -0.982 0.32611
## CBSA47260 8.331e-03 3.370e-02 0.247 0.80477
## CBSA47300 -3.046e-02 9.043e-02 -0.337 0.73621
## CBSA47380 9.507e-02 9.043e-02 1.051 0.29313
## CBSA47580 -1.627e-01 1.183e-01 -1.376 0.16889
## CBSA47644 7.739e-03 2.665e-02 0.290 0.77150
## CBSA47894 -2.308e-02 2.555e-02 -0.903 0.36630
## CBSA47940 3.127e-02 1.043e-01 0.300 0.76431
## CBSA48140 -1.786e-01 1.398e-01 -1.277 0.20154
## CBSA48300 1.892e-02 1.804e-01 0.105 0.91650
## CBSA48424 3.792e-02 3.422e-02 1.108 0.26774
## CBSA48540 -1.080e-02 9.031e-02 -0.120 0.90479
## CBSA48620 -1.040e-01 5.478e-02 -1.898 0.05769 .
## CBSA48660 3.701e-02 7.878e-02 0.470 0.63849
## CBSA48700 -2.247e-02 1.182e-01 -0.190 0.84921
## CBSA48864 8.832e-03 5.233e-02 0.169 0.86597
## CBSA48900 6.705e-02 5.739e-02 1.168 0.24265
## CBSA49020 -1.154e-01 1.398e-01 -0.826 0.40909
## CBSA49180 -7.099e-02 6.843e-02 -1.037 0.29957
## CBSA49340 -7.242e-02 5.389e-02 -1.344 0.17900
## CBSA49420 -8.664e-02 9.894e-02 -0.876 0.38122
## CBSA49620 8.453e-02 7.389e-02 1.144 0.25266
## CBSA49660 -3.370e-02 5.313e-02 -0.634 0.52594
## CBSA49700 -1.931e-01 1.563e-01 -1.236 0.21658
## CBSA49740 2.856e-02 1.284e-01 0.222 0.82395
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.09748577)
##
## Null deviance: 2446.5 on 16731 degrees of freedom
## Residual deviance: 1342.3 on 16338 degrees of freedom
## (175 observations deleted due to missingness)
## AIC: 12691
##
## Number of Fisher Scoring iterations: 5
CBSA’s significant for the outcome of TOTAL_VISITS>0 include:
| 99% CI | 12420 | Austin-Round Rock, TX | POSITIVE |
| 16700 | Charleston-North Charleston, SC | POSITIVE | |
| 17860 | Columbia, MO | POSITIVE | |
| 23580 | Gainesville, GA | POSITIVE | |
| 25060 | Gulfport-Biloxi-Pascagoula, MS | NEGATIVE | |
| 95% CI | 10180 | Abilene, TX | POSITIVE |
| 19180 | Danville, IL | NEGATIVE | |
| 19340 | Davenport-Moline-Rock Island, IA-IL | POSITIVE | |
| 20940 | El Centro, CA | POSITIVE | |
| 25180 | Hagerstown-Martinsburg, MD-WV | POSITIVE | |
| 26980 | Iowa City, IA | POSITIVE | |
| 29340 | Lake Charles, LA | POSITIVE | |
| 90% CI | 15380 | Buffalo-Cheektowaga-Niagara Falls, NY | POSITIVE |
| 16180 | Carson City, NV | POSITIVE | |
| 21660 | Eugene, OR | NEGATIVE | |
| 28740 | Kingston, NY | POSITIVE | |
Now, let’s plot the outcome of TOTAL_VISITS against the MEAN_ELIX_SCORE, creating a separate intercept for each CBSA.
ggplot(data=PUF_ELIX_IP2009_GT0, aes(x=MEAN_ELIX_SCORE, y=TOTAL_VISITS,
group=CBSA)) +
geom_line() +
geom_smooth(method = "glm", method.args=c(family="poisson"), se=FALSE)
## `geom_smooth()` using formula 'y ~ x'
#
# Poisson against the outcome of TOTAL_LOS (Total Length of Stay) for each CBSA
ggplot(data=PUF_ELIX_IP2009_GT0, aes(x=MEAN_ELIX_SCORE, y=TOTAL_LOS,
group=CBSA)) +
geom_line() +
geom_smooth(method = "glm", method.args=c(family="poisson"), se=FALSE)
## `geom_smooth()` using formula 'y ~ x'
Now, let’s try fitting some models with the random effect of CBSA (noting that there are several beneficiaries whose counties are too small to belong to a CBSA)
zero_cbsas <- PUF_ELIX_IP2009 %>% subset(CBSA=="0")
zero_fips <- PUF_ELIX_IP2009 %>% subset(FULL_FIPS_CODE=="0")
25,943 beneficiaries without CBSAs.
1,755 beneficiaries without FIPS.
PUF_ELIX_IP2009_GT0 <- PUF_ELIX_IP2009_GT0 %>%
mutate(MC_SCALED = scale(MEAN_CHRONIC))
PUF_ELIX_IP2009_GT0 <- PUF_ELIX_IP2009_GT0 %>%
mutate(TC_SCALED = scale(TOTAL_CODES))
PUF_ELIX_IP2009_GT0 <- PUF_ELIX_IP2009_GT0 %>%
mutate(LOS_SCALED = scale(TOTAL_LOS))
PUF_ELIX_IP2009_GT0 <- PUF_ELIX_IP2009_GT0 %>%
mutate(PHYS_SCALED = scale(TOTAL_PHYS))
PUF_ELIX_IP2009_GT0 <- PUF_ELIX_IP2009_GT0 %>%
mutate(ELIX_SCALED = scale(MEAN_ELIX_SCORE))
CBSA_GT0 <- subset(PUF_ELIX_IP2009_GT0, CBSA!="0")
Modeling 13,080 Beneficiaries with 1 or more inpatient visits in 2009 who live in a CBSA:
# Linear Random Effects Model ~ RE Slope: Elixhauser Score, RE Intercept: CBSA
lmm = lmer(TOTAL_VISITS ~ MC_SCALED + LOS_SCALED + ELIX_SCALED + B_DIED + (ELIX_SCALED|CBSA), data = CBSA_GT0)
## boundary (singular) fit: see ?isSingular
summary(lmm)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: TOTAL_VISITS ~ MC_SCALED + LOS_SCALED + ELIX_SCALED + B_DIED +
## (ELIX_SCALED | CBSA)
## Data: CBSA_GT0
##
## REML criterion at convergence: 16922
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6815 -0.5634 -0.1767 0.2737 5.8067
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## CBSA (Intercept) 0.0002498 0.01580
## ELIX_SCALED 0.0002179 0.01476 1.00
## Residual 0.2124769 0.46095
## Number of obs: 13080, groups: CBSA, 384
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.297e+00 4.292e-03 1.824e+02 302.116 < 2e-16 ***
## MC_SCALED 1.104e-01 4.192e-03 1.307e+04 26.331 < 2e-16 ***
## LOS_SCALED 3.032e-01 4.222e-03 1.307e+04 71.807 < 2e-16 ***
## ELIX_SCALED 5.054e-02 4.330e-03 2.062e+02 11.672 < 2e-16 ***
## B_DIED 2.188e-01 2.921e-02 1.307e+04 7.491 7.27e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) MC_SCA LOS_SC ELIX_S
## MC_SCALED -0.001
## LOS_SCALED 0.004 -0.232
## ELIX_SCALED 0.095 -0.087 -0.156
## B_DIED -0.132 0.002 -0.045 0.001
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
plot(lmm)
# GLM Random Effects Model, Gamma ~ RE Intercept: CBSA
glmm = glmer(TOTAL_VISITS ~ MC_SCALED + LOS_SCALED + ELIX_SCALED + B_DIED + (1|CBSA), data = CBSA_GT0, family = Gamma(link = "log"))
summary(glmm)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula: TOTAL_VISITS ~ MC_SCALED + LOS_SCALED + ELIX_SCALED + B_DIED +
## (1 | CBSA)
## Data: CBSA_GT0
##
## AIC BIC logLik deviance df.resid
## 9713.2 9765.6 -4849.6 9699.2 13073
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8196 -0.5961 -0.2683 0.1865 6.5000
##
## Random effects:
## Groups Name Variance Std.Dev.
## CBSA (Intercept) 0.001422 0.03771
## Residual 0.098513 0.31387
## Number of obs: 13080, groups: CBSA, 384
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 0.227911 0.004398 51.825 < 2e-16 ***
## MC_SCALED 0.077905 0.002604 29.915 < 2e-16 ***
## LOS_SCALED 0.193077 0.002766 69.793 < 2e-16 ***
## ELIX_SCALED 0.037110 0.002605 14.243 < 2e-16 ***
## B_DIED 0.132857 0.018120 7.332 2.27e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) MC_SCA LOS_SC ELIX_S
## MC_SCALED 0.002
## LOS_SCALED 0.003 -0.263
## ELIX_SCALED 0.004 -0.104 -0.178
## B_DIED -0.079 -0.003 -0.046 -0.002
plot(glmm)
anova(lmm, glmm)
## refitting model(s) with ML (instead of REML)
In this case, the Gamma mixed model has the best fit, with AIC 9713.2 and -log-likelihood -4849.6
Both models have the same number of parameters.
CBSA_GT0 <- CBSA_GT0 %>%
mutate(SCALED_COSTS = scale(ALLCOSTS))
# Random Effects Model ~ RE Slope: TOTAL_PHYS (Number of Physicians), RE Intercept: CBSA
lmm2 = lmer(TOTAL_LOS ~ MEAN_CHRONIC + TOTAL_CODES + TOTAL_PHYS + MEAN_ELIX_SCORE + SCALED_COSTS + (TOTAL_PHYS|CBSA), data = CBSA_GT0)
## boundary (singular) fit: see ?isSingular
summary(lmm2)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## TOTAL_LOS ~ MEAN_CHRONIC + TOTAL_CODES + TOTAL_PHYS + MEAN_ELIX_SCORE +
## SCALED_COSTS + (TOTAL_PHYS | CBSA)
## Data: CBSA_GT0
##
## REML criterion at convergence: 77595.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.4172 -0.5529 -0.1889 0.3470 9.0341
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## CBSA (Intercept) 4.1445 2.0358
## TOTAL_PHYS 0.9028 0.9502 -1.00
## Residual 21.4792 4.6346
## Number of obs: 13080, groups: CBSA, 384
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 9.136e-01 2.170e-01 6.463e+02 4.211 2.91e-05 ***
## MEAN_CHRONIC 1.172e-01 2.097e-02 1.287e+04 5.590 2.31e-08 ***
## TOTAL_CODES 3.303e-01 1.472e-02 1.305e+04 22.447 < 2e-16 ***
## TOTAL_PHYS 2.405e-01 9.904e-02 8.459e+02 2.428 0.0154 *
## MEAN_ELIX_SCORE 9.563e-02 2.058e-02 1.287e+04 4.646 3.42e-06 ***
## SCALED_COSTS 1.717e+00 7.058e-02 1.284e+04 24.330 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) MEAN_C TOTAL_C TOTAL_P MEAN_E
## MEAN_CHRONI -0.310
## TOTAL_CODES -0.064 -0.160
## TOTAL_PHYS -0.659 -0.034 -0.535
## MEAN_ELIX_S -0.181 -0.041 -0.180 0.048
## SCALED_COST 0.516 0.057 -0.328 -0.233 0.023
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
plot(lmm2)
CBSA plus the slope of number of physicians explains the majority of the variance.
The remaining variance is small, but is well-explained by the covariates.
The residuals are fairly equally distributed around the zero line.
Let’s scale variables, and compare it with a glmer.
# GLM Random Effects Model ~ RE Slope: PHYS_SCALED (Number of Physicians), RE Intercept: CBSA
glmm2 = glmer.nb(TOTAL_LOS ~ MC_SCALED + TC_SCALED + PHYS_SCALED + ELIX_SCALED + SCALED_COSTS + (PHYS_SCALED|CBSA), data = CBSA_GT0)
## boundary (singular) fit: see ?isSingular
summary(glmm2)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Negative Binomial(3.4561) ( log )
## Formula: TOTAL_LOS ~ MC_SCALED + TC_SCALED + PHYS_SCALED + ELIX_SCALED +
## SCALED_COSTS + (PHYS_SCALED | CBSA)
## Data: CBSA_GT0
##
## AIC BIC logLik deviance df.resid
## 69576.5 69651.3 -34778.3 69556.5 13070
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.6393 -0.7309 -0.2586 0.4263 8.5202
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## CBSA (Intercept) 7.041e-04 2.654e-02
## PHYS_SCALED 1.698e-10 1.303e-05 -0.87
## Number of obs: 13080, groups: CBSA, 384
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.743218 0.006475 269.202 < 2e-16 ***
## MC_SCALED 0.049163 0.006550 7.505 6.12e-14 ***
## TC_SCALED 0.332325 0.013244 25.093 < 2e-16 ***
## PHYS_SCALED 0.003009 0.012166 0.247 0.805
## ELIX_SCALED 0.040299 0.006256 6.442 1.18e-10 ***
## SCALED_COSTS 0.121043 0.009575 12.641 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) MC_SCA TC_SCA PHYS_S ELIX_S
## MC_SCALED -0.019
## TC_SCALED -0.052 -0.156
## PHYS_SCALED 0.006 -0.054 -0.677
## ELIX_SCALED -0.013 -0.025 -0.182 0.059
## SCALED_COST -0.005 0.056 -0.355 -0.262 0.024
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
plot(glmm2)
ANOVA Comparison:
anova(lmm2, glmm2)
## refitting model(s) with ML (instead of REML)
The glmer NB model has the superior fit, but this model doesn’t fit nearly as well as the visits model.
# LA COUNTY 06 037
county_subset <- CBSA_GT0 %>%
mutate(predictions = predict(glmm)) %>%
filter(FULL_FIPS_CODE=="6037")
Exploring LA County’s 320 Beneficiaries, using the TOTAL_VISITS Gamma model
ggplot(county_subset, aes(x = predictions, y = TOTAL_VISITS)) +
geom_point() +
xlab("Predicted TOTAL VISITS (glmer Gamma)") +
ylab("Total Visits") +
theme_classic()
ggplot(county_subset, aes(x =predictions, y = (TOTAL_VISITS-predictions))) +
geom_point() +
xlab("Predicted Total Visits (glmer Gamma)") +
ylab("Residuals") +
theme_classic()
The best-fitting model still under-predicts in general
ggplot(county_subset, aes(x = MC_SCALED, y = TOTAL_VISITS)) +
geom_point() +
stat_smooth(method = "lm", aes(color="linear"), se=FALSE) +
stat_smooth(method = "glm", aes(color="gamma"), method.args=list(family = Gamma(link = "log")), se=FALSE) +
stat_smooth(method = "glm.nb", aes(color="negative binomial"), se=FALSE) +
xlab("Mean Chronic Conditions (Scaled)") +
ylab("Number of Visits") +
theme_classic()
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
ggplot(county_subset, aes(x = ELIX_SCALED, y = TOTAL_VISITS)) +
geom_point() +
stat_smooth(method = "lm", aes(color="linear"), se=FALSE) +
stat_smooth(method = "glm", aes(color="gamma"), method.args=list(family = Gamma(link = "log")), se=FALSE) +
stat_smooth(method = "glm.nb", aes(color="negative binomial"), se=FALSE) +
xlab("Avg Elix Score (Scaled)") +
ylab("Total Visits") +
theme_classic()
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
ggplot(county_subset, aes(x = LOS_SCALED, y = TOTAL_VISITS)) +
geom_point() +
stat_smooth(method = "lm", aes(color="linear"), se=FALSE) +
stat_smooth(method = "glm", aes(color="gamma"), method.args=list(family = Gamma(link = "log")), se=FALSE) +
stat_smooth(method = "glm.nb", aes(color="negative binomial"), se=FALSE) +
xlab("Length of Stay (Scaled)") +
ylab("Total Visits") +
theme_classic()
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached